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 A146968 Brocard's problem: positive integers n such that n!+1 = m^2. 11
 4, 5, 7 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS No other terms below 10^9. See A085692 for more comments and references. - M. F. Hasler, Nov 20 2018 LINKS Berndt, B. C. and Galway, W. F. On the Brocard-Ramanujan Diophantine Equation n!+1=m^2, The Ramanujan Journal, March 2000, Volume 4, Issue 1, pp 41-42. Eric Weisstein's World of Mathematics, Brocard's Problem. EXAMPLE 7! + 1 = 5041 = 71^2, hence 7 is in the sequence. - Klaus Brockhaus, Nov 05 2008 MATHEMATICA Select[Range[10], IntegerQ[Sqrt[#!+1]]&] (* Harvey P. Dale, Jan 31 2015 *) PROG (Shell) #!/bin/sh n=0 while(true) do n=`echo \$n + 1 | bc` calc "(\$n! + 1)" ^ "(1 / 2)" | grep -v \. done (MAGMA) [ : n in [1..8047] | t where t, p:=IsSquare(Factorial(n)+1) ]; // Klaus Brockhaus, Nov 05 2008 (PARI) { for (n=1, 60100, if(issquare(n!+1) == 1, print(n) ) ) } \\ Marco Bellaccini (marcomurk(AT)tele2.it), Nov 08 2008 CROSSREFS A085692, A146968, A216071 are all essentially the same sequence. - N. J. A. Sloane, Sep 01 2012 Sequence in context: A166042 A321772 A333435 * A298982 A112247 A319260 Adjacent sequences:  A146965 A146966 A146967 * A146969 A146970 A146971 KEYWORD bref,nonn,hard AUTHOR Marco Bellaccini (marcomurk(AT)tele2.it), Nov 03 2008 EXTENSIONS Edited by Max Alekseyev, Feb 06 2010 STATUS approved

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Last modified September 21 02:11 EDT 2020. Contains 337266 sequences. (Running on oeis4.)